Understanding function of diminished chord in Paganini's 4th caprice
I'm trying to understand this simple progression in the middle of Paganini's 4th caprice.
This seems like I-?-I-V7-I in Eb major, but I am unable to figure out what the function of the second chord is. I know it is Ebdim7 (or Adim7 or Gbdim7 or Cdim7).
My attempts:
There is some nice voice leading from the A-nat to the B-flat in the third chord, which suggested it is a secondary leading chord of some sort, but the third chord is Eb, which doesn't make sense: io7 - I??
Perhaps the second chord could be viio7/V7, but this doesn't seem to make sense if there is a I chord between the viio7/V7 and the V7.
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This is a "common-tone diminished seventh chord". It's used, in this case, as an elaboration of the I chord. You can read more about it and see examples in a few SE questions:
Diminished chord constructed over the tonic degree?
A chord progression from Leavitt: how to analyze it correctly
How does this Bdim7 resolves to F/C?
Is this a harmonic sequence?
What's going on functionally/structurally in these four bars of Rachmaninoff's 3rd piano concerto?
Where does the Eb diminished 7 in I Wanna Be Around come from and how to play over it?
This is basically a better-phrased version of Albrecht Hügli's answer, but I'd treat the chord progression as this, with the diminished chord in bold:
Isus4 - I - vii°7/V - I6/4 - V7 - I
Yes, I'd treat the diminished 7th chord as a secondary dominant, especially since it resolves its root by step to I6/4, then V7. The I6/4 chord is so strongly associated with the V chord and resolves into a version of it so often that some textbooks (including one I learned from) call it V6/4 instead.
A,C,Eb,Gb (=vii o7) -> Bb,Eb,G (=I46) (resp. V46
The secondary VIIdim to the dominant (also interpreted as #IVdim ) usually in a I46 chord - like in your example.
e.g.:
Very common in Bach‘s recitatives!
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